Question

A brave child decides to grab on to an already spinning merry-go-round. The child is initially at rest and has a mass of 31.5 kg. The child grabs and clings to a bar that is 1.40 m from the center of the merry-go-round, causing the angular velocity of the merry-go-round to abruptly drop from 55.0 rpm to 17.0 rpm. What is the moment of inertia of the merry-go-round with respect to its central axis?

Answer 1

Law of Conservation Angular Momentum:

The angular momentum of the object does not change with adding or subtracting the mass from the rotating body because this change is immediately accompanied by the change in the rotation rate of the object, therefore, angular momentum remains conserved in an isolated system.

Where;

is Angular velocity and I is Moment of inertia.

Conservation angular momentum:

Sol:

Given data:

• m=31.5 kg be the mass of the child

• r=1.40 m be the radius of rotation of the child

• ωi = 55 rpm be the initial angular velocity of the merry-go-round

• ωf=17 rpm be the final angular velocity of the merry-go-round

Here as we know that total angular momentum is always conserved for child + round system.

So, by applying the law of conservation of angular momentum and we can get:

Therefore, the moment of inertia of the merry-go-round with respect to its central axis is 27.6 kgm2.